The description of the basic model of the trajectory motion of an aerospace vehicle (ASV) with a high finite thrust in the Earth’s gravitational field and atmosphere is given. Using relations from Chap. 1 , the optimality conditions for the Pontryagin maximum principle (PMP) is written down for such model. The control and phase constraints, which are typical for aerospace transportation systems, are taken into account, including those that go beyond the PMP formalism, such as the constraint on the rate of control vector change. The questions of the existence of a singular optimal control are discussed. Parallels are drawn between the conditions for the existence of the singular extreme surface obtained in a generalized phase space, and the Miele degenerate extremals. In order to have a base for comparing qualitative new optimal solutions obtained, the first two sections of this chapter describe the classical approximate optimal solutions by Okhotsimsky-Eneev-Lowden for a simplified model of motion in a uniform gravitational field and the gravitational turn mode.